{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:DQR6FFTWVAGQEMX26DX26MKKEJ","short_pith_number":"pith:DQR6FFTW","canonical_record":{"source":{"id":"2606.01159","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-31T11:06:06Z","cross_cats_sorted":["cs.GT"],"title_canon_sha256":"2ef96745c58f73b169c1e58f4eb80814fbe2c36ff253190649a8b4485b676e1a","abstract_canon_sha256":"449271b7085adca9b7239844a141c2d18b5f4dbf9e1e06e75b2478153bf6a7be"},"schema_version":"1.0"},"canonical_sha256":"1c23e29676a80d0232faf0efaf314a22627d9e70ba4980206b6fc4b384076193","source":{"kind":"arxiv","id":"2606.01159","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.01159","created_at":"2026-06-02T02:04:25Z"},{"alias_kind":"arxiv_version","alias_value":"2606.01159v1","created_at":"2026-06-02T02:04:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01159","created_at":"2026-06-02T02:04:25Z"},{"alias_kind":"pith_short_12","alias_value":"DQR6FFTWVAGQ","created_at":"2026-06-02T02:04:25Z"},{"alias_kind":"pith_short_16","alias_value":"DQR6FFTWVAGQEMX2","created_at":"2026-06-02T02:04:25Z"},{"alias_kind":"pith_short_8","alias_value":"DQR6FFTW","created_at":"2026-06-02T02:04:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:DQR6FFTWVAGQEMX26DX26MKKEJ","target":"record","payload":{"canonical_record":{"source":{"id":"2606.01159","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-31T11:06:06Z","cross_cats_sorted":["cs.GT"],"title_canon_sha256":"2ef96745c58f73b169c1e58f4eb80814fbe2c36ff253190649a8b4485b676e1a","abstract_canon_sha256":"449271b7085adca9b7239844a141c2d18b5f4dbf9e1e06e75b2478153bf6a7be"},"schema_version":"1.0"},"canonical_sha256":"1c23e29676a80d0232faf0efaf314a22627d9e70ba4980206b6fc4b384076193","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:25.356793Z","signature_b64":"SsFR5sfS+FRgWNfT7FOr1p289g2ja8NJg+frO79UjNyigCSoL7u05VHO1TT9duP1WQNpsnYTYP83wPxi5O1dBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c23e29676a80d0232faf0efaf314a22627d9e70ba4980206b6fc4b384076193","last_reissued_at":"2026-06-02T02:04:25.356363Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:25.356363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.01159","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-02T02:04:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"44kG8kUiwdchK6eWX0H9nP++Y8GVb5JUhHLYes5lwK440Z06XeaiY1lez2J3VRQ2m1oAzgTKLJAfsFTcvfkKDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:46:29.446635Z"},"content_sha256":"f52eb964f30f8c542ec43086f866bfd08fd4d814acb2020e6773ea8a65ddc0b7","schema_version":"1.0","event_id":"sha256:f52eb964f30f8c542ec43086f866bfd08fd4d814acb2020e6773ea8a65ddc0b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:DQR6FFTWVAGQEMX26DX26MKKEJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fairness in two-player zero-sum games with bandit feedback","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT"],"primary_cat":"cs.LG","authors_text":"Pratik Gajane, S Akash","submitted_at":"2026-05-31T11:06:06Z","abstract_excerpt":"We study two-player zero-sum games (TPZSGs) with bandit feedback under fairness constraints requiring every action to be played with probability at least $\\alpha/m$. Existing instance-dependent results target $\\textit{pure}$ Nash equilibria, while fairness generically produces $\\textit{mixed}$ equilibria, a harder learning target. Our key technical tool is a reparametrization: every fair strategy decomposes as $p = (\\alpha/m)\\mathbf{1} + (1-\\alpha)\\widetilde{p}$ with $\\widetilde{p} \\in \\Delta_m$, and substituting into the payoff form yields $p^{\\top}Aq = \\widetilde{p}^{\\top}\\widetilde{A} q$ fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01159","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.01159/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-02T02:04:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ojQeZ4apOPDQPm3v6ppO3rl0uUtSKNMNmCyciSiFMH5Wf6h5mdS1Qx2pbuAaWSAsxQaVHmwCqXfceOtRv9uhBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:46:29.447025Z"},"content_sha256":"269b21756bfe6998ead8bdcc137e2dd7cefce5261a5e7f82767c1369b6811075","schema_version":"1.0","event_id":"sha256:269b21756bfe6998ead8bdcc137e2dd7cefce5261a5e7f82767c1369b6811075"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DQR6FFTWVAGQEMX26DX26MKKEJ/bundle.json","state_url":"https://pith.science/pith/DQR6FFTWVAGQEMX26DX26MKKEJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DQR6FFTWVAGQEMX26DX26MKKEJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T08:46:29Z","links":{"resolver":"https://pith.science/pith/DQR6FFTWVAGQEMX26DX26MKKEJ","bundle":"https://pith.science/pith/DQR6FFTWVAGQEMX26DX26MKKEJ/bundle.json","state":"https://pith.science/pith/DQR6FFTWVAGQEMX26DX26MKKEJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DQR6FFTWVAGQEMX26DX26MKKEJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DQR6FFTWVAGQEMX26DX26MKKEJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"449271b7085adca9b7239844a141c2d18b5f4dbf9e1e06e75b2478153bf6a7be","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-31T11:06:06Z","title_canon_sha256":"2ef96745c58f73b169c1e58f4eb80814fbe2c36ff253190649a8b4485b676e1a"},"schema_version":"1.0","source":{"id":"2606.01159","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.01159","created_at":"2026-06-02T02:04:25Z"},{"alias_kind":"arxiv_version","alias_value":"2606.01159v1","created_at":"2026-06-02T02:04:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01159","created_at":"2026-06-02T02:04:25Z"},{"alias_kind":"pith_short_12","alias_value":"DQR6FFTWVAGQ","created_at":"2026-06-02T02:04:25Z"},{"alias_kind":"pith_short_16","alias_value":"DQR6FFTWVAGQEMX2","created_at":"2026-06-02T02:04:25Z"},{"alias_kind":"pith_short_8","alias_value":"DQR6FFTW","created_at":"2026-06-02T02:04:25Z"}],"graph_snapshots":[{"event_id":"sha256:269b21756bfe6998ead8bdcc137e2dd7cefce5261a5e7f82767c1369b6811075","target":"graph","created_at":"2026-06-02T02:04:25Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.01159/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study two-player zero-sum games (TPZSGs) with bandit feedback under fairness constraints requiring every action to be played with probability at least $\\alpha/m$. Existing instance-dependent results target $\\textit{pure}$ Nash equilibria, while fairness generically produces $\\textit{mixed}$ equilibria, a harder learning target. Our key technical tool is a reparametrization: every fair strategy decomposes as $p = (\\alpha/m)\\mathbf{1} + (1-\\alpha)\\widetilde{p}$ with $\\widetilde{p} \\in \\Delta_m$, and substituting into the payoff form yields $p^{\\top}Aq = \\widetilde{p}^{\\top}\\widetilde{A} q$ fo","authors_text":"Pratik Gajane, S Akash","cross_cats":["cs.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-31T11:06:06Z","title":"Fairness in two-player zero-sum games with bandit feedback"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01159","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f52eb964f30f8c542ec43086f866bfd08fd4d814acb2020e6773ea8a65ddc0b7","target":"record","created_at":"2026-06-02T02:04:25Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"449271b7085adca9b7239844a141c2d18b5f4dbf9e1e06e75b2478153bf6a7be","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-31T11:06:06Z","title_canon_sha256":"2ef96745c58f73b169c1e58f4eb80814fbe2c36ff253190649a8b4485b676e1a"},"schema_version":"1.0","source":{"id":"2606.01159","kind":"arxiv","version":1}},"canonical_sha256":"1c23e29676a80d0232faf0efaf314a22627d9e70ba4980206b6fc4b384076193","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c23e29676a80d0232faf0efaf314a22627d9e70ba4980206b6fc4b384076193","first_computed_at":"2026-06-02T02:04:25.356363Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:04:25.356363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SsFR5sfS+FRgWNfT7FOr1p289g2ja8NJg+frO79UjNyigCSoL7u05VHO1TT9duP1WQNpsnYTYP83wPxi5O1dBg==","signature_status":"signed_v1","signed_at":"2026-06-02T02:04:25.356793Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.01159","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f52eb964f30f8c542ec43086f866bfd08fd4d814acb2020e6773ea8a65ddc0b7","sha256:269b21756bfe6998ead8bdcc137e2dd7cefce5261a5e7f82767c1369b6811075"],"state_sha256":"5444c02f976cb1c73d72a6d360200013a195e609fe992ed54402dd88be31e07a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eW+SN9rMStuAHGKSWxYQseAcVPQ0tTWlkUgiPj4nRxqCcnhddirMI6y6t9g9VAjOw8/iMVmCHXm6XIJCwQdzBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T08:46:29.449101Z","bundle_sha256":"ce27805df8af3bc63008cd345e0ade265397483c5cb7562abc7502e7ea9d21ee"}}